Home
Class 11
MATHS
f: R^(+) rarr R is continuous function s...

`f: R^(+) rarr R` is continuous function satisfying `f(x/y)=f(x) - f (y) AA x, y in R^(+) `. If f'(1) = 1, then

A

f is unbounded

B

`lim_(x rarr0)f(1/x)=0`

C

`lim_(xrarr0)(f(1+x))/x=1`

D

`lim_(x rarr0)x.f(x)=0`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Promotional Banner

Topper's Solved these Questions

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (LECTURE SHEET (ADVANCED)) (Linked Comprehension Type Questions)|6 Videos

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II (LECTURE SHEET (ADVANCED)) (Integer Type Questions)|4 Videos

  • DIFFRENTATION

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - I (MAIN))(Straight Objective Typee Questions)|41 Videos

  • DIFFERENTIATION

    AAKASH SERIES|Exercise ADVANCED SUBJECTIVE TYPE QUESTIONS |26 Videos

  • DIRECTION COSINES & RATIOS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|36 Videos

Similar Questions

Explore conceptually related problems

Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) for all x, y in R . If f(2)=9 then f(3) is

Let 'f' be a non-zero real valued continuous function satisfying f(x + y) = f(x), f(y) . f(y) for all x, y in R if f(2) = 9 , then f(6) =

If f(x + y) = f(x) f(y) AA x, y and f(5) = 2, f'(0) = 3 then f'(5) =

If f : R to R is continuous such that f(x + y) = f(x) + f(y) x in R , y in R and f(1) = 2 then f(100) =

Let f:R to R be a continuous function and f(x)=f(2x) is true AA x in R . If f(1) = 3 then the value of int_(-1)^(1) f(f(x))dx=

Consider a real valued function f(x) satisfying 2f(xy)=(f(x))^(y)+(f(y))^(x) AA x , y in R and f(1)=a where a != 1 then (a-1) sum_(i=1)^(n) f(i)=